CAREER: Visualizing and Manipulating Anyons in 2D Topological Matter with Scanning Tunneling Microscopy

Non-technical Abstract: All particles in our three-dimensional universe are classified as either fermions or bosons. However, in two dimensions, more exotic variants are possible. This project investigates anyons, emergent particles in two-dimensional materials that are neither fermion nor boson. The exotic properties of anyons are not only fundamentally fascinating but also hold potential for future fault-tolerant quantum computing. The research team searches for signatures of anyons by developing novel microscopic methods and exploring new classes of quantum materials. In collaboration with outreach programs, the team excites public interest in quantum physics through hands-on demonstration tours. The project also modernizes university experimental physics education by incorporating quantum information and machine learning methods, and it establishes an online platform to make two-dimensional material preparation more accessible to a broader research community. Technical Abstract: Anyons, predicted in topological systems such as the fractional quantum Hall effects, exhibit behaviors governed by their unique quantum statistics. Theory suggests that exchanging two abelian anyons results in a fractional phase shift, while exchanging two non-abelian anyons causes a unitary transformation. Non-abelian anyons feature highly degenerate ground states that are topologically protected from perturbations and can only be altered through particle exchanges, known as braiding, making them excellent candidates for fault-tolerant quantum computing. Although recent interferometry experiments have advanced in detecting abelian anyons, capturing signatures of non-abelian quantum statistics requires more than just extensions of current methods. In this project, the research team utilizes a scanning tunneling microscope (STM) to probe and manipulate anyons. This method allows the team to directly visualize anyon wavefunctions, reveal their abelian and non-abelian statistics, and gather valuable real-space information. More importantly, the project leverages STM-induced potentials to manipulate the position of anyons while conducting interferometry, facilitating the demonstration of non-abelian anyon braiding. Furthermore, the project investigates fractional Chern insulators—the zero-field counterparts of the fractional quantum Hall effect—using STM to elucidate the origins of their spontaneous topological properties and potentially enable access to anyons without the need for large magnetic fields. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.